Generalization of exactly-solvable model to exhibit solid-fluid phase transition in crystal structures with two particles in a primitive cell

In our previous paper (Komatsu 2015 J. Stat. Mech. P08020), we investigated an interacting-particle model with infinite-range cosine potentials, and derived the partition function which shows solid-fluid phase transition by exact calculation. However, we could treat only simple lattice structures in which more than one stable point exists in a primitive cell such as the triangular or face-centered cubic lattice. In the present paper, we generalize our previous scheme to more complicated lattice structures with two particles in a primitive cell. Generalization to more complicated lattice structures is straightforward.